A company makes hanging ornaments in various shapes. The heights of the ornaments are shown. Using a calculator, order these ornaments from tallest to shortest.

Question

3 shapes are shown side by side: an equilateral triangle, a rhombus, and a square. Each has a vertical line that bisects it. Each has a hook-like shape extending from the top. Measurements labels are included for the bisecting line and an exterior face. The base of the triangle is labeled 4 inches and the bisecting line is labeled 2 times start root 3 end root inches. The side of the rhombus is labeled 3 inches and the bisecting line is labeled 3 times starts root 2 end root inches. The side of the square is labeled 4 inches and the bisecting line is labeled 4 inches.

(1 point)
Responses

square, diamond, triangle
square, diamond, triangle

diamond, square, triangle
diamond, square, triangle

triangle, square, diamond
triangle, square, diamond

square, triangle, diamon

Answer 1

Let's calculate the heights of each of the ornaments based on the given measurements:

1. Triangle:

   • The height is given as $2\sqrt{3}$ inches.

2. Rhombus:

   • The height is given as $3\sqrt{2}$ inches.

3. Square:

   • The height is given as $4$ inches.

Now we will compare the numerical values of the heights.

• Height of the triangle: $$2\sqrt{3}\approx 2\times 1.732\approx 3.464\text{ inches}$$

• Height of the rhombus: $$3\sqrt{2}\approx 3\times 1.414\approx 4.242\text{ inches}$$

• Height of the square: $$4\text{ inches}$$

Now, we can order these from tallest to shortest:

1. Rhombus (approximately 4.242 inches)
2. Square (4 inches)
3. Triangle (approximately 3.464 inches)

Thus, the correct order from tallest to shortest is:

diamond, square, triangle.

So, the correct response is: diamond, square, triangle.